# Math Help - optimzation problem #4

1. ## optimzation problem #4

A chain of stores has been selling a line of cameras for 50 dollars each and has been averaging sales of 8000 cameras a month. They decide to increase the price, but their market research indicates that for each one dollar increase in price, sales will fall by 100.

a) find the demand function

b)find the price that will maximize their revenue

2. Originally Posted by skeske1234
A chain of stores has been selling a line of cameras for 50 dollars each and has been averaging sales of 8000 cameras a month. They decide to increase the price, but their market research indicates that for each one dollar increase in price, sales will fall by 100.

a) find the demand function

b)find the price that will maximize their revenue
let x = number of $1 price increases demand function ... d = 8000 - 100x revenue = demand * price ... R = (8000-100x)(50+x) find dR/dx and determine the value of x that maximizes revenue ... don't forget that the price is (50+x). 3. Originally Posted by skeeter let x = number of$1 price increases

demand function ...

d = 8000 - 100x

revenue = demand * price ...

R = (8000-100x)(50+x)

find dR/dx and determine the value of x that maximizes revenue ... don't forget that the price is (50+x).
ok.. question, your demand function is d=8000-100x
and b) they have $9.50....... I got 50+15=65 dollars with the demand function i used from above(yours: d=8000-100x) I am not sure how they got their answers.. 4. I get a price of$65 (\$15 increase) to maximize revenue also.